Coloring of three-dimensional printed objects

ABSTRACT

A method of printing a three-dimensional (3D) color object, layer-by-layer, comprises: obtaining a 3D CAD specification defining a 3D geometry and a surface color distribution for the color object to be printed, defining regions on a surface of the color object; defining colors for each region based on the CAD specification; determining, using the 3D geometry of the specification, conditions applying at respective regions that are liable to cause color variation, such that using the colors as defined at the respective regions may give rise to a coloration error; selecting color corrections defined for respective determined conditions; correcting the defined colors; and printing the 3D color object with the color corrections.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.15/112,729 filed on Jul. 20, 2016, which is a National Phase of PCTPatent Application No. PCT/IL2015/050087 having International FilingDate of Jan. 26, 2015, which claims the benefit of priority under 35 USC§ 119(e) of U.S. Provisional Patent Application No. 61/931,634 filed onJan. 26, 2014. The contents of the above applications are allincorporated by reference as if fully set forth herein in theirentirety.

FIELD AND BACKGROUND OF THE INVENTION

The present invention, in some embodiments thereof, relates to coloringof three-dimensional printed objects and, more particularly, but notexclusively, to a method of ensuring uniformity of individual colors ina multi-colored object.

In three-dimensional printing, an object is formed by selectivedeposition of layers using a 3D printing device. In many cases amulti-colored object is required, and art is known for producingmulti-colored objects from a 3D printer. In general, transparent orwhite material is used to make the object and different faces of theobject face different directions. The overall perceived color iscontributed to by the surface layers and the layers immediatelyunderneath and this gives rise to the problem, that at junctions betweenfaces, or in thin parts of the structure where opposites faces are closetogether, colors from other regions may interfere to give a non-uniformcolor effect. Likewise radiation, such as UV radiation that may be usedto cure the colors, may not radiate evenly over differentially-facingsurfaces, or may be blocked or shaded from reaching some parts of the 3Dobjects.

Color uniformity has been dealt with in standard two-dimensionalprinting, but the issue of angles and adjoining faces does not apply.Furthermore, although a printing substrate may sometimes be transparent,if printing on opposite faces, an opaque substrate is used.

Color uniformity has also been dealt with in conventional manufacture.However, in conventional manufacture a prototype is built and thencoloration can be corrected if needed. In three-dimensional printing theinitial prototype is the final object and thus no such color correctionoption is typically available.

SUMMARY OF THE INVENTION

The present embodiments relate to making an initial selection of colorsat individual pixels to compensate for the non-uniformity effects.

According to an aspect of some embodiments of the present inventionthere is provided a method of printing a three-dimensional (3D) colorobject, layer-by-layer, the method comprising:

-   -   obtaining a 3D CAD specification defining a 3D geometry and a        surface color distribution for the color object;    -   defining regions on a surface of the color object;    -   defining colors for each region based on the surface color        distribution;    -   determining, using the 3D geometry, conditions applying at        respective regions that are liable to cause color variation,        such that using the colors as defined at the respective regions        may give rise to a coloration error;    -   selecting color corrections defined for respective determined        conditions;    -   correcting the defined colors using the defined corrections, to        compensate for respectively corresponding coloration errors; and    -   printing the 3D color object using respective corrected defined        colors at each region.

In an embodiment, the color is printed over surface pixels and theconditions comprise colors in neighboring pixels.

In an embodiment, the color corrections are obtained from a look uptable.

In an embodiment, the object is printed using a material having at leastsome transparency, color perception being defined by a depth into thesurface, and each surface pixel being defined in terms of apredetermined number of voxels extending into the depth in a colorstack, the condition being interference between different color stacksof neighboring 3D surfaces.

An embodiment may comprise obtaining the respective corrections from alook-up table defined for a corresponding color interference.

An embodiment may comprise obtaining the respective correction using acolor change model.

An embodiment may comprise obtaining the respective correction using adithering process between voxels of respectively interfering colorstacks.

An embodiment may comprise generating different voxel combinations forrespective pairs of interfering color stacks and finding a combinationgiving a least error with a design color.

In an embodiment, the finding a combination giving a least errorcomprises matching the respective different voxel combinations to find acombination requiring a minimal amount of voxel overwriting.

In an embodiment, the finding a combination giving a least errorcomprises placing least strong colors in voxel positions of maximalmutual interference.

In an embodiment, the conditions comprise either of surface angle andsurface position relative to other surfaces.

An embodiment may comprise obtaining the corrections from a look uptable defined for the member.

An embodiment may comprise:

obtaining the corrections by printing a test 3D object under theconditions; and

tabulating measured color deviations against applied colors.

An embodiment may comprise:

obtaining the corrections by obtaining factors responsible for causingerrors under predetermined conditions;

calculating errors using the obtained factors; and

tabulating the calculated errors against the conditions.

An embodiment is provided for dealing with discontinuity issues thatarise with bright colors or colors of high luminance. The methodinvolves detecting the presence of bright colors or colors of highluminance, and where these bright or high luminance colors are detected,applying as corrections an outer layer of white and an underlying coreof white on either side of a layer of the bright or high luminancecolors

According to a second aspect of the present invention there is provideda three-dimensional (3D) color printer for printing 3D color objectslayer-by-layer, the printer comprising:

-   -   a specification input for inputting a 3D CAD specification        defining a 3D geometry and a surface color distribution for the        color object;    -   a region definer for defining regions on a surface of the color        object;    -   a color definer for defining colors for each region based on the        surface color distribution;    -   an error determination unit for determining, using the 3D        geometry, conditions applying at respective regions that are        liable to cause color variation, such that using the colors as        defined at the respective regions may give rise to a coloration        error;    -   a selector, for selecting color corrections defined for        respective determined conditions;    -   a corrector for correcting the defined colors using the defined        corrections, to compensate for respectively corresponding        coloration errors; and    -   the printer being configured to print the 3D color object using        respective corrected defined colors at each region.

Unless otherwise defined, all technical and/or scientific terms usedherein have the same meaning as commonly understood by one of ordinaryskill in the art to which the invention pertains. Although methods andmaterials similar or equivalent to those described herein can be used inthe practice or testing of embodiments of the invention, exemplarymethods and/or materials are described below. In case of conflict, thepatent specification, including definitions, will control. In addition,the materials, methods, and examples are illustrative only and are notintended to be necessarily limiting.

Implementation of the method and/or system of embodiments of theinvention can involve performing or completing selected tasks manually,automatically, or a combination thereof. Moreover, according to actualinstrumentation and equipment of embodiments of the method and/or systemof the invention, several selected tasks could be implemented byhardware, by software or by firmware or by a combination thereof usingan operating system.

For example, hardware for performing selected tasks according toembodiments of the invention could be implemented as a chip or acircuit. As software, selected tasks according to embodiments of theinvention could be implemented as a plurality of software instructionsbeing executed by a computer using any suitable operating system. In anexemplary embodiment of the invention, one or more tasks according toexemplary embodiments of method and/or system as described herein areperformed by a data processor, such as a computing platform forexecuting a plurality of instructions. Optionally, the data processorincludes a volatile memory for storing instructions and/or data and/or anon-volatile storage, for example, a magnetic hard-disk and/or removablemedia, for storing instructions and/or data. Optionally, a networkconnection is provided as well. A display and/or a user input devicesuch as a keyboard or mouse are optionally provided as well.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Some embodiments of the invention are herein described, by way ofexample only, with reference to the accompanying drawings. With specificreference now to the drawings in detail, it is stressed that theparticulars shown are by way of example and for purposes of illustrativediscussion of embodiments of the invention. In this regard, thedescription taken with the drawings makes apparent to those skilled inthe art how embodiments of the invention may be practiced.

In the drawings:

FIG. 1 is a simplified flow chart illustrating a method of correctingcolors on a 3D printed object according to a preferred embodiment of thepresent invention;

FIG. 2A is a simplified diagram illustrating an empirical method ofobtaining the color corrections for different conditions for use in themethod of FIG. 1;

FIG. 2B is a simplified diagram illustrating a method of carrying outcolor correction according to an embodiment of the present invention inwhich the error-causing condition relates to interfering colors inneighboring pixels;

FIG. 3 is a simplified diagram illustrating a method of obtaining colorcorrections for the method of FIG. 1 or FIG. 2B, using analyticaltechniques;

FIG. 4 is a simplified diagram illustrating an alternative method ofcarrying out color correction according to an embodiment of the presentinvention in which the error-causing condition relates to interferingcolors in neighboring pixels;

FIG. 5 is a simplified diagram illustrating a further alternative methodof carrying out color correction according to an embodiment of thepresent invention in which the error-causing condition relates tointerfering colors in neighboring pixels;

FIG. 6 is a simplified diagram showing an assumption used in colorcorrection according to the present embodiments;

FIG. 7 is a simplified diagram illustrating the problem of not usingcolor correction;

FIG. 8 is a simplified diagram showing an example of how differentarrangements of voxels in a color stack can lead to the same surfacecolors;

FIG. 9 is a simplified diagram illustrating dithering according to themethod of FIG. 5;

FIG. 10 is a simplified diagram illustrating a further example ofdithering according to the method of FIG. 5;

FIG. 11 is a simplified diagram illustrating a method of building up alook up table for color correction in the case of conditions that aredue to radiation exposure susceptibility and the like of the givenobject surface;

FIG. 12 is a simplified diagram illustrating a method of colorcorrection for conditions that are due to radiation exposuresusceptibility and the like; and

FIG. 13 is a simplified flow chart illustrating a method of colorcorrection specifically for bright colors according to an embodiment ofthe present invention.

DESCRIPTION OF SPECIFIC EMBODIMENTS OF THE INVENTION

The present invention, in some embodiments thereof, relates to coloringof three-dimensional printed objects and, more particularly, but notexclusively, to a method of ensuring uniformity of individual colors ina multi-colored object.

Color corrections are applied over the object to correct for conditionsdetermined from the 3D geometry that are liable to cause colorationerrors.

Before explaining at least one embodiment of the invention in detail, itis to be understood that the invention is not necessarily limited in itsapplication to the details of construction and the arrangement of thecomponents and/or methods set forth in the following description and/orillustrated in the drawings and/or the Examples. The invention iscapable of other embodiments or of being practiced or carried out invarious ways.

Referring now to the drawings, FIG. 1 is a simplified flow chart whichshows a method of correcting colors on a three-dimensional (3D) colorobject, which is then printed layer-by-layer and colored using the colorcorrections.

Box 10 indicates obtaining a 3D CAD specification defining a 3D geometryand a surface color distribution for the object to be printed andcolored.

Additionally, in some implementations, color is defined at the surfaceof an object, so that not just each location on the surface but alsodifferent angles relative to the normal at the location may becharacterized by their own color properties.

Regions on the surface of the color object, typically areas sharing thesame color and geometry, are defined, as per box 12.

The colors for each region are assigned based on the surface colordistribution provided by the CAD specification, as per box 14.

Again, using the CAD specification, the 3D geometry is used to determineconditions applying at the different regions that are liable to causecolor variation. In other words the geometry is scanned to find caseswhere using the colors as defined at the respective regions may giverise to a coloration error. For example, if two opposite surfaces aretoo close together, the colors may interfere. If the surfaces areawkwardly angled or hidden behind other parts, curing radiation may notreach the region.

In box 18, color corrections are obtained for the determined conditions.

-   -   The corrections may be calculated or may be obtained from        look-up tables, as will be described in greater detail below.

In box 20, the colors are redefined using the obtained corrections, tocompensate for the conditions and corresponding errors obtained in stage18.

Finally, in stage 22, the object is printed using the corrected colorsat each region.

The conditions causing errors may for example comprise colors present inneighboring pixels or voxels. As will be explained in greater detailbelow, the object may be printed using a material which is typicallywhite or otherwise opaque but having some transparency. Color perceptionis thus affected by all colors within a depth into the surface. Eachsurface pixel can therefore have its color defined in terms of a certainnumber of voxels extending into the depth and forming what is referredto herein as a color stack, so that the condition causing color errormay be interference between different color stacks of neighboring 3Dsurfaces. In particular, particularly at sharp edges or over thin parts,color stacks from the different surfaces may coincide.

The method may comprise obtaining corrections from a look-up tabledefined for a corresponding color interference. Alternatively thecorrection may be obtained using a color change model, or may involveusing a dithering process between voxels of respectively interferingcolor stacks.

The method may involve generating different voxel combinations forrespective pairs of interfering color stacks and finding a combinationgiving a least error with a design color, as explained in greater detailhereinbelow in respect of FIG. 9 and other figures. Thus, for example,the combination giving a least error may be obtained by matching thedifferent voxel combinations to find a combination requiring a minimalamount of voxel overwriting.

Alternatively, as discussed in FIG. 8, hereinbelow, the combinationgiving a least error, may be obtained by placing least strong colors invoxel positions of maximal mutual interference. The term “least strongcolors” includes lighter colors and colors of higher luminance.

Alternatively, the conditions may be surface angle, or surface positionrelative to other surfaces, and the error may be due to differentexposures to curing radiation and the like. As before, the correctionmay be obtained from a look up table defined for the specific condition,say the given radiation exposure.

One way of obtaining the corrections is empirically, as shown in FIG.2A, by printing a test 3D object under said conditions, and tabulatingmeasured color deviations against applied colors.

An alternative way of obtaining the corrections is analytically, as perFIG. 3, by obtaining factors responsible for causing errors underpredetermined conditions, calculating errors using the obtained factors,and tabulating the calculated errors against the conditions.

A further method of dealing with errors comprises separation of themodel into three layers, an outer layer which is white, a middle layerin color, and the core in white. This has benefit in quality on subtlecolor changes. The input may be a vignette, characterized by the absenceof abrupt color changes between neighbouring locations. It is, however,a desirable attribute of the printing process that no such abruptchanges are introduced as an artifact when none existed in the input.Nevertheless the kind of errors discussed herein include artifacts thatare introduced when there are abrupt changes between different lightcolors or colors of high luminance, those colors that are close towhite. The use of white layers above and below may remove suchartifacts.

In greater detail, color repeatability in 3D printing is relativelyaccurate when comparing different material batches or different printersand print events. However, the coloring may exhibit larger tintdeviations over the different regions of the printed geometry. One ofthe reasons for color deviation is a cross-talk between proximatesurfaces of thin geometries, i.e. the influence of one color surface onanother due to the partial transparency of the color material.

The present embodiments may account for the expected color deviationsand may then modulate the color composition in order to obtain optimalappearance of the final parts.

The appearance of a 3D printed color part is typically a result of thecomposition of the outer regions of the printed part. Since the printedmaterials are not completely opaque and have some degree oftransparency, the visible color depends not only on the outermostmaterial segment, that is the droplet or voxel or combination ofdroplets or voxels, but also on further in material segments. The extentof depth to which the underlying colored segments affect the partappearance may be termed as the extinction depth. Naturally, theextinction depth is proportional to the transparency of the coloredmaterial. Thus, for a given part and given set of color materials we candefine an outer region, i.e. color shell, which determines the part'sappearance. The thickness of the shell may be about equal to theextinction depth of the given materials.

When materials of different color are placed inside the color shellvolume, their overall optical properties, such as light refraction,reflection, absorption, diffusion, etc. may be considered in order topredict the resulting surface color. The appearance of each point on thesurface is dictated by the stack of underlying color material segments,i.e. color stack. It should be noted that in thin geometries some colormaterial segments may affect more than one surface—e.g. in a thin wallthe inner segments may affect both opposite faces of the wall. That isto say two different surfaces may share the same color stack. Thisphenomenon is commonly termed as color cross-talk.

Therefore, in order to produce a correct representation of color in 3Dprinted parts, the present embodiments provide ways to relate the coloras it appears in a point on the part surface to the composition of theunderlying color stack. One way of obtaining such a relationship is byusing an analytical approach, where the optical parameters of the colorstack components are fed into the appropriate physical equations.Another way is by using an empirical approach, where the different stackvariations are printed and measured by colorimeter.

Once the relationship between the composition of the color stack and thevisible color is established, it is possible to populate the color shellwith color stacks to match the required colors. Frequently during thepopulation two or more color stacks may collide, especially when thepart geometry contains thin features and/or when the extinction depth islarge. In this case an algorithm may be used to refine the availablecolor stacks and find the combination that optimally satisfies therequirements of all surfaces.

Reference is now made to FIG. 2A, which is a simplified diagram showingan example of the empirical method discussed above, namely a method forcolor 3D printing which involves building a look up table using colormeasurements.

In FIG. 2A, color calibration targets are printed using various colorstack compositions 110. Then the resulting colors are measured 112, sayusing color spectrophotometry, spectrophotometry and placed in the lookup table 114. The color value may be represented in any suitable way,including standard RGB color coordinates or CIE Lab, HSL, LCH or anyother.

Reference is now made to FIG. 2B, which is a simplified flow diagramshowing how to use the resulting LUTs to calculate the required printedcolor stack composition for each region of the color shell.

Initially, the CAD file describing the 3D geometry and its color textureis received 120.

Then the geometry is divided 122 into a core and a color shell.

Subsequently, the color shell is divided—box 124—into volumetricregions.

Then the LUTs are used—box 126—to assign each region with a color stackthat results in an optimal (i.e. min dE) reproduction of the requestedcolors.

The design is tested for conflicts between color stacks 128, to findinstances in which the color stack for one region enters the color stackof another region. That is to say it is possible to determine and markaccordingly all regions where colors stacks conflict, by studying the 3Dgeometry that was determined in boxes 120 and 122.

If there are no such regions then the procedure finishes 130. In case ofconflict between adjacent color stacks, one option is to select acombination of color stacks that optimally reproduce the requestedcolors. Another option involves color dithering as will be discussed ingreater detail below.

Reference is now made to FIG. 3, which is a simplified flow chartshowing an example of a method for color 3D printing using theanalytical method discussed above.

The method comprises determining 140 the optical characteristics for allcolor material components used in the 3D printing, in particular thelayering material and the color components but also any coatings and anyother materials that may be involved.

A range of color stacks is provided 142. Then the opticalcharacteristics are used analytically to calculate the resulting colorsfor each of the color stacks in the range 144. It may be possible toexpress the results as a mathematical model or formula. However it isnot always possible to arrive at such a model and if not then a look-uptable LUT may be constructed—146.

The look up table or model is then used as discussed above in respect ofFIG. 2B.

Reference is now made to FIG. 4 which illustrates a method of building acolor stack when the materials in the 3D object are at least somewhattransparent and the color stacks interfere with each other.

The problem definition is to find a method to color thin walls to havedifferent colors on either side, and the color on each face appearing asintended irrespective of the color on the opposite side.

In the method, a color stack having a depth of n voxels is defined topaint the wall with a non-transparent color. Any wall having a thickness<2*n has a problem of being colored from both sides if the colors aredifferent since both sides share some of the pixels of the color stack.

A table or model may be used to directly specify the appearance of alimited library of color combinations. Consider a three-way corner atthe intersection of three colored planes. For six basic colors there areabout a 100 interesting combinations of colors for the corner. This is amanageable number, and one possibility is to provide a factory solutionfor each variation, say as a lookup table. A real model may comprisecorners of arbitrary color, and interpolation or heuristics can then beused to supplement the lookup table. For example given a set of colorseach side needs in its stack, one may order the stack so that thelighter colors are placed in the inner layers, so that the shared colorshave as small an influence as possible.

Referring now to FIG. 4, for the case of conflicting color stacks 150,one takes each model to be printed and to be colored with a given set ofinks and decomposes 152 the model definition into a set of corners.

Each corner may be composed of a set of facets, and may be a thin wallof substantially parallel facets. For each corner a library of cornersas described above is consulted to find—as per box 154—the best match inthe library or from the model.

A distance is then measured—box 156—between the specified color and thecolor provided by the library. Distance measure may be according tocriteria including a measure of distance of color per facet.

The library provided color stack is then modified to better fit theactual color specified, and two alternatives for such modification areshown in alternate boxes 158 and 160.

The method of box 158 uses a model predicting color change as a functionof inks.

-   For example:-   To increase Lab a*, add magenta ink-   To increase Lab b*, add yellow ink-   To decrease Lab L*, add black ink and-   To increase Lab L*, add white ink

The method of box 160 uses heuristics. For example one may place lightercolored ink at the inner layers of the stack where the highestinterference occurs, to minimize that interference.

It is noted that if the wall is thicker, so that only two facets have asignificant influence on the voxel color then a much simplified modelmay be used.

Reference is now made to FIG. 5 which illustrates dithering, again foruse where there are conflicts between color stacks.

The 3D object may typically be built from white and somewhat transparentmodel material, surrounded by a colored depth region, where the coloreddepth region makes up the color stack. As before, the question is how tocolor the stack when parts of the stack are shared with other surfaces.

The support color may be chosen to provide the best match to thedesigned object surface color. As discussed, the color diffuses via thelayers immediately under the surface, distorting the color.

The aim is to find 170 a dithering vector that provides a best match.FIG. 9 below shows a worked example of the method of FIG. 5. FIG. 9shows examples of different dithering vectors that can be selected.

In constructing the vectors, each surface color may be presented by asize n (n=6 in the example) dithering vector of voxels which aresemi-transparent. One may assume a very simple mathematic model wherethe influence of voxels on the final color geometrically decreases whilepixels go deeper inside model. More complicated models may take intoaccount the different size and transparency of voxel on differentdirections.

For every color channel we may calculate the color according toC=C1+C2/a+C3/a*a+ . . . Cn/(a{tilde over ( )}n)(1), where Cn can be 0 or1.

A thick wall is defined as a wall with thickness n*V<T<2*n*V, (V thevoxel size). In such walls the dithering vectors for opposite sidesintersect and can be combined. For a wall <n*V we can decrease the nparameter.

In box 172 one calculates the color produced by every combination ofvoxels and then in box 174 finds an error with respect to the requireddesign color. It is noted that there are 2^(n) possibilities, which is amanageable number in computing when n<10. The number of possibilitiesmay be decreased if necessary using certain heuristics, depending on therequired surface color.

After calculating the color and error the good matches are combined inthe separate channels into single vectors. In order to determine thegood matches the vectors are ordered in box 176 according to the errorsfound above, and only the good vectors in the upper part of the list areselected for combining.

In box 178 having found those combinations with small enough errors overthe desired colors on both surfaces, we now look for those vectors whichhave the same tails, that is have common colors in the inner part of thecolor stack so that when they overwrite, no changes need to be made. Ifthere is such a vector combination then the combination is selected asthe best fit. If there is no such combination then the combination withthe longest length common tail is selected instead, so that minimumoverwriting is needed. The size of tail can be calculated for every wallas K=2*n−T/V+1. The chosen vectors provide a dither, thus unifying theirK-tails.

A sort of brute force alternative to the above may be used when themodel of surface colors starts to deviate from the separate in-depthvoxel colors, or the required calculations are too complex. Predefinedvectors with different lengths (from n to 2*n) may be used which producethe best possible saturated colors from both sides. Such vectors mayproduce the colors on either side, and then brightness and saturationcan be provided by adding black and white pixels.

FIGS. 6-9 illustrate different examples of relating a color stack todesired colors on oppositely facing thin walls.

FIG. 6 illustrates an initial assumption. A design color 200 leads togeneration of a color stack 202. Color stack 202 generates surfacecolors 204. The printed pixels are partially transparent, so that aspecific color can be formed by overlay of pixels of different colors.The same green color is formed from an overlay of yellow-cyan orcyan-yellow.

That is to say, the assumption is that the exact order, meaning whichcolor is on the surface and which color is underneath, has onlysecondary importance, slightly affecting the shade of the resultingcolor but no more.

In FIG. 7 the design faces require the colors shown in block 206. Thetransparency goes beyond just a couple of pixels and can cause crosstalk between adjacent areas of a geometry. Color stack 208 is set upnaively to provide each surface with the correct color but ignoring theopposite surface and the adjoining pixels. In this case, both facetshave reduced saturation, due to the presence of underlying colors, andthe end result 210 is quite different from the design result 206.

Reference is now made to FIG. 8, which shows four different options forgenerating a specified pair of colors for opposite sides of a thin wall.Specifically, a target 220 requires a left face in green and a rightface in orange, Green being Cyan+Yellow, and orange beingMagenta+Yellow.

Four possible solutions are shown. In option 222 the wall colors areformed with the yellow pixels inside as common colors on the inside ofthe stack, and cyan/magenta outside.

In option 224, the wall colors are formed with the yellow pixels outsideand cyan/magenta inside.

In options 226 and 228, the wall colors are formed with one column ofyellow pixels outside and the other inside.

If each wall, or facet, is dithered separately, without taking inaccount adjacent facets, the resulting arrangement can be any one of thefour options 222 to 228, or a mix between these options. But the mostaccurate color reproduction is achieved in option 222, where theunderlying color is mutual for both of the facets, thus resulting inminimal cross-talk. In fact the solution of 222 satisfies the commontails algorithm of FIG. 5 and also the heuristic solution of option box160 in FIG. 4, where the lightest colors are placed in the middle.

FIG. 9 is an example using the tail matching algorithm of FIG. 5 above.This example shows that a smart refining of dithering options, thattakes into account all collisions between neighboring dithering stackscan produce an optimal arrangement, where the final CMY composition overthe two surfaces is more consistent with the requested value. The designtarget is an object 230 being 9 pixels wide and having different colorson opposite facets. The system uses CMY parent colors, and a typicaldithering depth=6 pixels.

Five left facet dithering options are shown, 232 where Color1, thetarget color=2C+2M+2Y.

Five right facet dithering options are shown where color2=1C+2M+3Y.

Item 236 shows the five resulting arrangements when the two 6 px-deepdithering are combined, and in the event of conflict, the left option isoverwritten by the right. At 238, matching pixels of 236 are shown in afirst shading and replaced pixels are shown in a second shading. Version#5 does not require any replacement of pixels, all are green, and thushas the best match.

Reference is now made to FIG. 10, which is a simplified diagram showinga further series of five dithering options for two specified colors onopposite faces. 240 shows five left facet dithering options for aColor1=2C+1M+3Y. 242 shows five right facet dithering options for acolor2=1C+2M+3Y. 246 shows the combination vectors, and 238 shows that,in this case, all pairs make perfect match. Thus we can refine the bestoption according to additional parameters. For example, we may preferhaving the brightest color inside, therefore choosing arrangement #5.

As mentioned above, while color reproduction is relatively accurate(dE<3) when comparing different material batches or different printersand print events, it may exhibit larger tint deviations (dE<8) over thedifferent regions of the printed geometry. Another reason for thesedeviations, other than interference between pixels in the color stack,is to do with the orientation of the printed surfaces, the presence ofneighbor support material (glossy or matte) and the amount of UVexposure.

Fortunately, the resulting color shade is frequently related to the partgeometry and the tray layout, in which neighboring part geometries mayaffect UV exposure, for example, in a predictable way. The presentembodiments thus account for the expected color deviations anddynamically modulate the colorant balance to compensate for the anglesand the layout, thereby to aim at a uniform appearance of the finalparts.

Currently, the simplest way to form different colors is to populate theprinted voxels in a random manner according to a lookup table (LUT) thatcorrelates between the requested color and the correspondingconcentrations of each component. A red color, for example, may beformed by mixing 40% Magenta and 60% Yellow. The LUT is prepared byprinting different compositional variations and measuring their color.

In addition, the precise coloring is applied only to the outer region,the surface and immediate sub-surface of the part, as discussed above,while the inner bulk composition has no importance and can be constantor can vary depending on considerations that are not relevant to thepresent embodiments. A color correction for a given part region may thusinvolve modification of the requested concentrations in the outer,surface, regions of the part. Such regions are actually thin volumesthat extend along the normal to a point on the part's surface.

There are different ways to introduce the color corrections. Onepossible way is building different LUTs for different print variations.The tables may be built using empirical measurement of the situation.Consider the UV exposure example. To make an effective color correctionstrategy, one may print a target to be used for the LUT calculationunder minimal, medium and high UV exposures. The color deviations andrequired corrections are placed in the table for the differentconditions.

Then the 3D CAD design for a specific object is provided. Each point onthe surface geometry for a given tray is analyzed to calculate theexpected UV exposure. Then the requested color value of the point isread and translated into requested color concentrations using therelevant LUT that matches the expected radiation exposure.

Reference is now made to FIG. 11 which illustrates a flow chart forbuilding the LUT. The method for color 3D printing comprises buildingthe LUT to relate color value for example, RGB, CIE Lab, RGB, Grey Valueor any other suitable way of representing color, to actual printed colorcomposition (CMY, white, black or other) by printing color calibrationtargets that contain various printed color compositions—box 250—exposingto different printing conditions such as radiation doses, box 252, andmeasuring the resulting color value using a colorimetry device, box 254.The measurements against the color compositions are tabulated togetherin the LUT, box 256.

The LUT building process is then repeated for different printingconditions, such as UV exposure level, sample orientation on tray orprint mode (gloss/matte).

Reference is now made to FIG. 12, which illustrates using the resultingLUTs to calculate the required printed colors composition for eachregion of the geometry, according to its expected printing conditions.

Box 260 indicates receiving the CAD file describing a 3D geometry andthe corresponding requested color value.

Optional stage 262 indicates dividing the geometry into a core and anouter shell.

Box 264 indicates dividing the geometry into regions. Optionally, onlythe outer shell of the geometry will be divided into regions.

For each region box 266 indicates calculating the expected printingconditions.

Each region is then populated with voxels of parent color materials,while calculating the printed colors composition according to the LUTsthat corresponds to the expected printing conditions of the region.

Reference is now made to FIG. 13, which is a simplified flow chartillustrating a further embodiment of the present invention. In FIG. 13 afurther method of dealing with errors comprises determining whether themodel 300 contains 302 bright colors or colors of high luminance. If sothen the model is divided 304 into three layers, an outer layer which iswhite, a middle layer in color, and the core in white. This has benefitin quality on subtle color changes. The input may be a vignette,characterized by the absence of abrupt color changes betweenneighbouring locations. It is, however, a desirable attribute of theprinting process that no such abrupt changes are introduced as anartifact when none existed in the input. Nevertheless the kind of errorsdiscussed herein include artifacts that are introduced when there areabrupt changes between different light colors, those colors that areclose to white. The use of white layers above and below may remove suchartifacts.

In greater detail, the printing process introduces a strongnon-linearity in color reproduction with light colors, so that thederivative of output color vs. input color is much larger than one. Forexample the function relating output colors vs. input color may be y=xto the power of ⅓, where both are normalized so they range from 0 to 1.The derivative of y=x^(1/3) is

$y^{\prime} = \frac{1}{3x^{\frac{2}{3}}}$

which goes to infinity at x=0, so when x=0,

$\frac{dy}{dx} = {{infinity}.}$

The solution is to modify the printing process as shown in FIG. 13.

In an embodiment there is no user control whatsoever. The systemautomatically detects that a color is close to 0, and applies theoutlined solution.

The terms “comprises”, “comprising”, “includes”, “including”, “having”and their conjugates mean “including but not limited to”.

The term “consisting of” means “including and limited to”.

As used herein, the singular form “a”, “an” and “the” include pluralreferences unless the context clearly dictates otherwise.

It is appreciated that certain features of the invention, which are, forclarity, described in the context of separate embodiments, may also beprovided in combination in a single embodiment, and the abovedescription is to be construed as if this combination were explicitlywritten. Conversely, various features of the invention, which are, forbrevity, described in the context of a single embodiment, may also beprovided separately or in any suitable subcombination or as suitable inany other described embodiment of the invention, and the abovedescription is to be construed as if these separate embodiments wereexplicitly written. Certain features described in the context of variousembodiments are not to be considered essential features of thoseembodiments, unless the embodiment is inoperative without thoseelements.

Although the invention has been described in conjunction with specificembodiments thereof, it is evident that many alternatives, modificationsand variations will be apparent to those skilled in the art.Accordingly, it is intended to embrace all such alternatives,modifications and variations that fall within the spirit and broad scopeof the appended claims.

All publications, patents and patent applications mentioned in thisspecification are herein incorporated in their entirety by referenceinto the specification, to the same extent as if each individualpublication, patent or patent application was specifically andindividually indicated to be incorporated herein by reference. Inaddition, citation or identification of any reference in thisapplication shall not be construed as an admission that such referenceis available as prior art to the present invention. To the extent thatsection headings are used, they should not be construed as necessarilylimiting. In addition, any priority document(s) of this applicationis/are hereby incorporated herein by reference in its/their entirety.

What is claimed is:
 1. A method of printing a three-dimensional (3D)color object comprising: obtaining a 3D CAD file defining a 3D geometryand a color texture for said color object; dividing said 3D geometryinto a core and a color shell; dividing said color shell into volumetricregions; calculating expected printing conditions for each of thevolumetric regions; populating each of the volumetric regions with colorvoxels providing an intended color according to a lookup table (LUT) ofcolor values against actual printed color composition under differentprinting conditions; and printing said 3D color object.
 2. The method ofclaim 1, comprising constructing said LUT by: printing color calibrationtargets using actual printed color compositions while exposing todifferent printing conditions; measuring the resulting color value foreach of said targets using a colorimetry device; and tabulating themeasured color values against the actual printed color composition andthe respective printing conditions.
 3. The method of claim 1, whereinsaid printing conditions are selected from UV exposure level, sampleorientation on tray, gloss/matte print mode, and any combinationthereof.
 4. The method of claim 1, wherein said actual printed colorcompositions are based on C, M, Y, white and black color materials. 5.The method of claim 1, wherein said color values are represented by oneof RGB color coordinates, CIE Lab coordinates, HSL, LCH and Grey Values.6. The method of claim 1, wherein the thickness of said color shell iscalculated relative to an extinction depth of the color materials used.7. A method of printing a three-dimensional (3D) color objectcomprising: obtaining a 3D CAD file defining a 3D geometry and a colorvalue for said color object; dividing said 3D geometry into volumetricregions; calculating expected printing conditions for each of thevolumetric regions; populating each of the volumetric regions with colorvoxels providing an intended color according to a lookup table (LUT) ofcolor values against actual printed color composition under differentprinting conditions; and printing said 3D color object.
 8. The method ofclaim 7, comprising constructing said LUT by: printing color calibrationtargets using actual printed color compositions while exposing todifferent printing conditions; measuring the resulting color value foreach of said targets using a colorimetry device; and tabulating themeasured color values against the actual printed color composition andthe respective printing conditions.
 9. The method of claim 7, whereinsaid printing conditions are selected from UV exposure level, sampleorientation on tray, gloss/matte print mode, and any combinationthereof.
 10. The method of claim 7, wherein said actual printed colorcompositions are based on C, M, Y, white and black color materials. 11.The method of claim 7, wherein said color values are represented by oneof RGB color coordinates, CIE Lab coordinates, HSL, LCH and Grey Values.